TSTP Solution File: NUM410+1 by SuperZenon---0.0.1
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- Process Solution
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% File : SuperZenon---0.0.1
% Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 14:42:13 EDT 2022
% Result : Theorem 2.88s 3.05s
% Output : Proof 2.88s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM410+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 5 15:12:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.88/3.05 % SZS status Theorem
% 2.88/3.05 (* PROOF-FOUND *)
% 2.88/3.05 (* BEGIN-PROOF *)
% 2.88/3.05 % SZS output start Proof
% 2.88/3.05 1. (relation T_0) (-. (relation T_0)) ### Axiom
% 2.88/3.05 2. (function T_0) (-. (function T_0)) ### Axiom
% 2.88/3.05 3. (relation T_0) (-. (relation T_0)) ### Axiom
% 2.88/3.05 4. (function T_0) (-. (function T_0)) ### Axiom
% 2.88/3.05 5. (ordinal (relation_dom T_0)) (-. (ordinal (relation_dom T_0))) ### Axiom
% 2.88/3.05 6. (-. (transfinite_sequence T_0)) (transfinite_sequence T_0) ### Axiom
% 2.88/3.05 7. ((transfinite_sequence T_0) <=> (ordinal (relation_dom T_0))) (-. (transfinite_sequence T_0)) (ordinal (relation_dom T_0)) ### Equiv 5 6
% 2.88/3.05 8. (((relation T_0) /\ (function T_0)) => ((transfinite_sequence T_0) <=> (ordinal (relation_dom T_0)))) (ordinal (relation_dom T_0)) (-. (transfinite_sequence T_0)) (function T_0) (relation T_0) ### DisjTree 3 4 7
% 2.88/3.05 9. (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (relation T_0) (function T_0) (-. (transfinite_sequence T_0)) (ordinal (relation_dom T_0)) ### All 8
% 2.88/3.05 10. (-. (subset (relation_rng T_0) (relation_rng T_0))) ### Refl(subset)
% 2.88/3.05 11. (-. (transfinite_sequence_of T_0 (relation_rng T_0))) (transfinite_sequence_of T_0 (relation_rng T_0)) ### Axiom
% 2.88/3.05 12. ((transfinite_sequence_of T_0 (relation_rng T_0)) <=> (subset (relation_rng T_0) (relation_rng T_0))) (-. (transfinite_sequence_of T_0 (relation_rng T_0))) ### Equiv 10 11
% 2.88/3.05 13. (((relation T_0) /\ ((function T_0) /\ (transfinite_sequence T_0))) => ((transfinite_sequence_of T_0 (relation_rng T_0)) <=> (subset (relation_rng T_0) (relation_rng T_0)))) (-. (transfinite_sequence_of T_0 (relation_rng T_0))) (ordinal (relation_dom T_0)) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (function T_0) (relation T_0) ### DisjTree 1 2 9 12
% 2.88/3.05 14. (All B, (((relation B) /\ ((function B) /\ (transfinite_sequence B))) => ((transfinite_sequence_of B (relation_rng T_0)) <=> (subset (relation_rng B) (relation_rng T_0))))) (relation T_0) (function T_0) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (ordinal (relation_dom T_0)) (-. (transfinite_sequence_of T_0 (relation_rng T_0))) ### All 13
% 2.88/3.05 15. (All A, (All B, (((relation B) /\ ((function B) /\ (transfinite_sequence B))) => ((transfinite_sequence_of B A) <=> (subset (relation_rng B) A))))) (-. (transfinite_sequence_of T_0 (relation_rng T_0))) (ordinal (relation_dom T_0)) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (function T_0) (relation T_0) ### All 14
% 2.88/3.05 16. (-. (((relation T_0) /\ (function T_0)) => ((ordinal (relation_dom T_0)) => (transfinite_sequence_of T_0 (relation_rng T_0))))) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) (All A, (All B, (((relation B) /\ ((function B) /\ (transfinite_sequence B))) => ((transfinite_sequence_of B A) <=> (subset (relation_rng B) A))))) ### ConjTree 15
% 2.88/3.05 17. (-. (All A, (((relation A) /\ (function A)) => ((ordinal (relation_dom A)) => (transfinite_sequence_of A (relation_rng A)))))) (All A, (All B, (((relation B) /\ ((function B) /\ (transfinite_sequence B))) => ((transfinite_sequence_of B A) <=> (subset (relation_rng B) A))))) (All A, (((relation A) /\ (function A)) => ((transfinite_sequence A) <=> (ordinal (relation_dom A))))) ### NotAllEx 16
% 2.88/3.05 % SZS output end Proof
% 2.88/3.05 (* END-PROOF *)
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